We address the problem of density estimation with $\bL_p$--loss by selection
of kernel estimators. We develop a selection procedure and derive
corresponiding $\bL_p$--risk oracle inequalities. It is shown that the proposed
selection rule leads to the minimax estimator that is adaptive over a scale of
the anisotropic Nikol'ski classes. The main technical tools used in our
derivations are uniform bounds on the $\bL_p$--norms of empirical processes
developed recently in Goldenshluger and Lepski~(2010).